Anyone replaced the vinyl flooring?

Hmmm...this is really interesting. We want to remove the carpet in our bedroom and put down some sort of vinyl flooring. Dogs ... 2 of them ... yes we wash them ... but they're dogs and they smell like dogs. And the hair is woven into the carpet. The vacuum gets more hair up by friction and static than suction.

Here's the problem ... we can NOT put 1/4 round down. At least not in front of the slide. SO ... if the self adhesive doesn't work ... how are we going to do this? I had really hoped the self stick would work for us.